JAMA : A Java Matrix Package

Background

JAMA is a basic linear algebra package for Java. It provides user-level
classes for constructing and manipulating real, dense matrices. It is
meant to provide sufficient functionality for routine problems, packaged in a
way that is natural and understandable to non-experts. It is intended to
serve as the standard matrix class for Java, and will be proposed as
such to the Java
Grande Forum and then to Sun.
A straightforward public-domain reference implementation has been developed by
the MathWorks and NIST as a strawman for such a class. We
are releasing this version in order to obtain public comment. There is no
guarantee that future versions of JAMA will be compatible with this one.

A sibling matrix package,
Jampack,
has also been developed at NIST and the University of Maryland. The
two packages arose from the need to evaluate alternate designs for
the implementation of matrices in Java. JAMA is based on a single
matrix class within a strictly object-oriented framework. Jampack
uses a more open approach that lends itself to extension by the
user. As it turns out, for the casual user the packages differ
principally in the syntax of the matrix operations. We hope you will
take the time to look at Jampack along with JAMA. There is much to
be learned from both packages.

Capabilities.

The Matrix class provides the fundamental operations of numerical linear
algebra. Various constructors create Matrices from two dimensional
arrays of double precision floating point numbers. Various gets
and sets provide access to submatrices and matrix elements.
The basic arithmetic operations include matrix addition and multiplication,
matrix norms and selected element-by-element array operations. A
convenient matrix print method is also included.

Five fundamental matrix decompositions, which consist of pairs or triples
of matrices, permutation vectors, and the like, produce results in five
decomposition classes. These decompositions are accessed by the Matrix
class to compute solutions of simultaneous linear equations, determinants,
inverses and other matrix functions. The five decompositions are

Cholesky Decomposition of symmetric, positive definite matrices

LU Decomposition (Gaussian elimination) of rectangular matrices

QR Decomposition of rectangular matrices

Eigenvalue Decomposition of both symmetric and nonsymmetric
square matrices

Singular Value Decomposition of rectangular matrices

The current JAMA deals only with real matrices. We expect that future versions
will also address complex matrices. This has been deferred since crucial
design decisions cannot be made until certain issues regarding the
implementation of complex in the Java language are resolved.

The design of JAMA represents a compromise between the need for pure
and elegant object-oriented design and the need to enable high performance
implementations.

Reference Implementation.

The implementation of JAMA downloadable
from this site is meant to be a reference implementation only.
As such, it is pedagogical in nature. The algorithms employed are
similar to those of the classic Wilkinson and Reinsch Handbook, i.e. the
same algorithms used in
EISPACK,
LINPACK
and
MATLAB.
Matrices are stored internally as native Java arrays
(i.e., double[][]).
The coding style is straightforward and readable. While the reference
implementation itself should provide reasonable execution speed for small
to moderate size applications, we fully expect software vendors and Java
VMs to provide versions which are optimized for particular environments.

Not Covered.

JAMA is by no means a complete linear algebra
environment. For example, there are no provisions for matrices with
particular structure (e.g., banded, sparse) or for more specialized
decompositions (e.g. Shur, generalized eigenvalue).
Complex matrices are not included.
It is not our intention to ignore these important problems. We expect
that some of these (e.g. complex) will be addressed in future versions.
It is our intent that the design of JAMA not preclude extension to some
of these additional areas.

Finally, JAMA is not a general-purpose array class. Instead, it
focuses on the principle mathematical functionality required to do numerical
linear algebra. As a result, there are no methods for array operations
such as reshaping or applying elementary functions (e.g. sine, exp, log)
elementwise. Such operations, while quite useful in many applications,
are best collected into a separate array class.

Previous versions

Request for Comments

JAMA was originally created as a proof-of-concept;
a potential primary linear algebra package that could be adopted for Java.
As such, it is no longer actively developed to keep track of evolving usage
patterns in the Java language, nor to further improve the API.
We will, however, fix outright errors in the code.

Discussion Group.

A discussion group has been established for such comments.
Comments and suggestions sent to
jama@nist.gov
will automatically be sent to the JAMA authors, as well as to all subscribers.
To subscribe, send email to
listproc@nist.gov
containing the text

[Note: NIST will not use the email addresses provided for any
purpose other than the maintenance of this discussion list. Participants may
remove themselves at any time by sending an email message to
listproc@nist.gov containing the text

Copyright Notice

This software is a cooperative product of The MathWorks and the National
Institute of Standards and Technology (NIST) which has been released to the
public domain. Neither The MathWorks nor NIST assumes any responsibility
whatsoever for its use by other parties, and makes no guarantees, expressed
or implied, about its quality, reliability, or any other characteristic.

Related Links & Libraries

As Jama is in the public domain
other developers are free to adopt and adapt this code
to other styles of programming or to extend or modernize the API.
You might find one of these libraries to be more suitable to your purposes.
Make note, however, that NIST makes no endorsement of these projects. We are currently aware of the following ports of Jama: